Advertisements
Advertisements
प्रश्न
Show that the points (2, 0), (–2, 0) and (0, 2) are vertices of a triangle. State the type of triangle with reason.
Advertisements
उत्तर
Let the points be P(2, 0), Q(–2, 0) and R(0, 2).
Distance between two points = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
By distance formula,
d(P, Q) = `sqrt([(-2) - 2]^2 + (0 - 0)^2`
= `sqrt((-4)^2 + (0)^2`
= `sqrt(16 + 0)`
= 4 ...(i)
d(Q, R) = `sqrt([0 - (-2)]^2 + (2 - 0)^2`
= `sqrt((2)^2 + (2)^2`
= `sqrt(4 + 4)`
= `sqrt(8)` ...(ii)
d(P, R) = `sqrt((0 -2)^2 + (2 - 0)^2`
= `sqrt((- 2)^2 + (2)^2`
= `sqrt(4 + 4)`
= `sqrt(8)` ...(iii)
On adding (ii) and (iii),
d(P, Q) + d(Q, R) = `4 + sqrt(8)`
`4 + sqrt(8) > sqrt(8)`
∴ d(P, Q) + d(Q, R) > d(P, R)
∴ Points P, Q, R are non colinear points.
We can construct a triangle through 3 non collinear points.
∴ The segment joining the given points form a triangle.
Since P(Q, R) = P(P, R)
∴ ∆PQR is an isosceles triangle.
∴ The segment joining the points (2, 0), (–2, 0) and (0, 2) will form an isosceles triangle.
APPEARS IN
संबंधित प्रश्न
Find the distance between two points
(i) P(–6, 7) and Q(–1, –5)
(ii) R(a + b, a – b) and S(a – b, –a – b)
(iii) `A(at_1^2,2at_1)" and " B(at_2^2,2at_2)`
Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (−3, 4).
Find the distance between the following pair of points:
(asinα, −bcosα) and (−acos α, bsin α)
Find the values of x, y if the distances of the point (x, y) from (-3, 0) as well as from (3, 0) are 4.
A(–8, 0), B(0, 16) and C(0, 0) are the vertices of a triangle ABC. Point P lies on AB and Q lies on AC such that AP : PB = 3 : 5 and AQ : QC = 3 : 5. Show that : PQ = `3/8` BC.
Find the distance of the following points from the origin:
(i) A(5,- 12)
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is ______.
Find the distance between the following pair of point in the coordinate plane :
(5 , -2) and (1 , 5)
Find the distance of a point (7 , 5) from another point on the x - axis whose abscissa is -5.
Find the distance between P and Q if P lies on the y - axis and has an ordinate 5 while Q lies on the x - axis and has an abscissa 12 .
Find the point on the x-axis equidistant from the points (5,4) and (-2,3).
Find the co-ordinates of points on the x-axis which are at a distance of 17 units from the point (11, -8).
Show that the points P (0, 5), Q (5, 10) and R (6, 3) are the vertices of an isosceles triangle.
Show that the points A (5, 6), B (1, 5), C (2, 1) and D (6, 2) are the vertices of a square ABCD.
KM is a straight line of 13 units If K has the coordinate (2, 5) and M has the coordinates (x, – 7) find the possible value of x.
Find distance of point A(6, 8) from origin.
If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is ______.
The points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.
Point P(0, 2) is the point of intersection of y-axis and perpendicular bisector of line segment joining the points A(–1, 1) and B(3, 3).
The points A(–1, –2), B(4, 3), C(2, 5) and D(–3, 0) in that order form a rectangle.
